Question

complete the following proof using definitions and properties. (2 pts per blank) given: st ⊥ hl, prove: ∠sth ≅ ∠stl statements reasons 1. st ⊥ hl given 2. ∠sth and ∠stl are right angles 3. ∠sth ≅ ∠stl

Explanation:

Step1: Recall perpendicular - definition

If $\overline{ST}\perp\overline{HL}$, then by the definition of perpendicular lines, the angles formed are right - angles. So, $\angle STL$ and $\angle STH$ are right angles.

Step2: Recall right - angle congruence

All right angles are congruent. Since $\angle STL$ and $\angle STH$ are right angles, $\angle STL\cong\angle STH$.

Answer:

1. $\overline{ST}\perp\overline{HL}$ (Given)
2. $\angle STL$ and $\angle STH$ are right angles (Definition of perpendicular lines)
3. $\angle STL\cong\angle STH$ (All right angles are congruent)